ดาวน์โหลด All Proceeding - AS Nida

Saving Cost
Saving Cost
Fig3. d versus discount for Model A
Fig4. d versus discount for Model B
5. Conclusion
The optimal order quantity and backorder are investigated
for model of defective items under one-time-only discount and pure
backordering. From numerical examples, the results show that 1) the
firm should always order when discount occur at the ordering point 2)
when discount is offered after the screening process and inventory is
positive, the firm should order when discount is large enough 3) when
unit discount is increases the firm should order more and increase the
amount of backorder 4) when purchasing cost is decreases firm should
order more and increase the amount of backorder.
Appendix A
To prove Theorem 1, we first construct saving cost that is
( a) a a
D = NTcn − NTcs.
(9)
It is easy to check that saving cost is convex. Next step is to
find optimal Qs and Bs by take first derivative of D (a) with respect to Qs and Bs then set them equal to zero, we obtain
d
d
222
( a)
∂D
Tc
pQ
= −[( c− d + s) + 2( c−d) h
*
∂Qs
Qn
x
*
Qs(1 − p) −Bn
+ ( c−d) h(1 − p)(
)] = 0,
D
and
∂D
+
∂B
x
( a)
s
*
Tcn p( In = − [( c+ s) + 2ch
*
Qn
Bs)
*
In(1 − p) − pBs Bs
− chp( ) + ( c − d) b ] = 0.
D D
Solve for Q s and B s we get (3) and (4) respectively.
s
(10)
(11)
References
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[3] M. Khan et al., “A review of the extensions of a modified EOQ
model for imperfect quantity items”, Int. J. of Production
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[4] H.M. Wee et al., “Optimal inventory model for items with
imperfect quality and shortage backordering”, Omega 35, 7-11,
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[5] H.-C. Chang and C.-H. Ho, “Exact closed-form solutions for
“optimal inventory model for items with imperfect quality and
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